Flow Deflection Angle using Prandtl Meyer Function Calculator

✖Prandtl Meyer Function at Downstream Mach no. is the Prandtl Meyer Functional value at downstream of expansion wave.ⓘ Prandtl Meyer Function at Downstream Mach no. [v_M2]			+10% -10%
✖Prandtl Meyer Function at Upstream Mach no. is the Prandtl Meyer Functional value at upstream of expansion wave.ⓘ Prandtl Meyer Function at Upstream Mach no. [v_M1]			+10% -10%

✖Flow Deflection Angle is defined as the angle by which the flow turns through the expansion wave.ⓘ Flow Deflection Angle using Prandtl Meyer Function [θ_e]

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Flow Deflection Angle using Prandtl Meyer Function Solution

STEP 0: Pre-Calculation Summary

Formula Used

Flow Deflection Angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no.
θ_e = v_M2-v_M1
This formula uses 3 Variables

Variables Used

Flow Deflection Angle - (Measured in Radian) - Flow Deflection Angle is defined as the angle by which the flow turns through the expansion wave.
Prandtl Meyer Function at Downstream Mach no. - (Measured in Radian) - Prandtl Meyer Function at Downstream Mach no. is the Prandtl Meyer Functional value at downstream of expansion wave.
Prandtl Meyer Function at Upstream Mach no. - (Measured in Radian) - Prandtl Meyer Function at Upstream Mach no. is the Prandtl Meyer Functional value at upstream of expansion wave.

STEP 1: Convert Input(s) to Base Unit

Prandtl Meyer Function at Downstream Mach no.: 83 Degree --> 1.44862327915502 Radian (Check conversion here)
Prandtl Meyer Function at Upstream Mach no.: 77 Degree --> 1.34390352403538 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_e = v_M2-v_M1 --> 1.44862327915502-1.34390352403538

Evaluating ... ...

θ_e = 0.10471975511964

STEP 3: Convert Result to Output's Unit

0.10471975511964 Radian -->5.99999999999999 Degree (Check conversion here)

FINAL ANSWER

5.99999999999999 ≈ 6 Degree <-- Flow Deflection Angle

(Calculation completed in 00.004 seconds)

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Home » Physics » Aerodynamics » Compressible Flow » Oblique Shock and Expansion Waves » Aerospace » Expansion Waves » Flow Deflection Angle using Prandtl Meyer Function

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Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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< Expansion Waves Calculators

Pressure behind Expansion Fan

LaTeX Go Pressure Behind Expansion Fan = Pressure Ahead of Expansion Fan*((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1))

Pressure Ratio across Expansion Fan

LaTeX Go Pressure Ratio Across Expansion Fan = ((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1))

Temperature behind Expansion Fan

LaTeX Go Temperature Behind Expansion Fan = Temperature Ahead of Expansion Fan*((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))

Temperature Ratio across Expansion Fan

LaTeX Go Temperature Ratio Across Expansion Fan = (1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2)

Flow Deflection Angle using Prandtl Meyer Function Formula

LaTeX Go

Flow Deflection Angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no.
θ_e = v_M2-v_M1

What is expansion wave?

When a supersonic flow is turned away from itself an expansion wave is formed. The fan continuously opens in the direction away from the corner. The expansion wave is in the shape of a fan centered at the corner.

How to Calculate Flow Deflection Angle using Prandtl Meyer Function?

Flow Deflection Angle using Prandtl Meyer Function calculator uses Flow Deflection Angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no. to calculate the Flow Deflection Angle, The Flow deflection angle using Prandtl Meyer function formula relates the Mach number to the maximum deflection angle achievable through an isentropic (constant entropy) expansion process. It is obtained as the difference of the Prandtl Meyer function calculated at downstream and upstream Mach number. Flow Deflection Angle is denoted by θ_e symbol.

How to calculate Flow Deflection Angle using Prandtl Meyer Function using this online calculator? To use this online calculator for Flow Deflection Angle using Prandtl Meyer Function, enter Prandtl Meyer Function at Downstream Mach no. (v_M2) & Prandtl Meyer Function at Upstream Mach no. (v_M1) and hit the calculate button. Here is how the Flow Deflection Angle using Prandtl Meyer Function calculation can be explained with given input values -> 343.7747 = 1.44862327915502-1.34390352403538.

FAQ

What is Flow Deflection Angle using Prandtl Meyer Function?

The Flow deflection angle using Prandtl Meyer function formula relates the Mach number to the maximum deflection angle achievable through an isentropic (constant entropy) expansion process. It is obtained as the difference of the Prandtl Meyer function calculated at downstream and upstream Mach number and is represented as θ_e = v_M2-v_M1 or Flow Deflection Angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no.. Prandtl Meyer Function at Downstream Mach no. is the Prandtl Meyer Functional value at downstream of expansion wave & Prandtl Meyer Function at Upstream Mach no. is the Prandtl Meyer Functional value at upstream of expansion wave.

How to calculate Flow Deflection Angle using Prandtl Meyer Function?

The Flow deflection angle using Prandtl Meyer function formula relates the Mach number to the maximum deflection angle achievable through an isentropic (constant entropy) expansion process. It is obtained as the difference of the Prandtl Meyer function calculated at downstream and upstream Mach number is calculated using Flow Deflection Angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no.. To calculate Flow Deflection Angle using Prandtl Meyer Function, you need Prandtl Meyer Function at Downstream Mach no. (v_M2) & Prandtl Meyer Function at Upstream Mach no. (v_M1). With our tool, you need to enter the respective value for Prandtl Meyer Function at Downstream Mach no & Prandtl Meyer Function at Upstream Mach no and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Flow Deflection Angle?

In this formula, Flow Deflection Angle uses Prandtl Meyer Function at Downstream Mach no & Prandtl Meyer Function at Upstream Mach no. We can use 1 other way(s) to calculate the same, which is/are as follows -

Flow Deflection Angle = (sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number Behind Expansion Fan^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number Behind Expansion Fan^2-1)))-(sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number Ahead of Expansion Fan^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number Ahead of Expansion Fan^2-1)))

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